Using Animation Nodes with the expression node with equation starting with x(n+1)=
It is like an iterative process to calculate the equations you have mentioned in your question. Thus, at step 1 (n = 1), we supply some initial value for (x, y) say (x0, y0) and calculate the equations or (x1, y1) then in step 2 (n=1), we will use the previous (x1, y1) to calculate the equations (x2, y2), and so on. Therefore, we have to store the calculated value of (x, y) during each iteration step. 

In animation nodes, the loop node has feature is called Reassign (see Advanced Node Settings in the N-panel) to store data per iteration that we can use in the next iteration. In this image, I have reassigned (or reinitialize) the vector input that acts as x(n), y(n) for the next iteration i.e., x(n+1), y(n+1).


Then animate the (a) parameter using Animate Float Node,




Here is Blend File: